To control an object to an arbitrary position or an arbitrary rotation, or to control to drive an object at an arbitrary velocity, the position of the object is measured by a sensor, and driving of the object is controlled on the basis of the measurement value.
For example, a semiconductor exposure apparatus comprises a stage which supports a wafer to be exposed to a pattern and can be driven at an arbitrary position, rotation, and velocity. A position measurement sensor for this stage is a laser interferometer (see, e.g., Japanese Patent Laid-Open No. 2002-319541). The current position, rotation, and velocity of the stage are calculated on the basis of the measurement value of the laser interferometer. To control the stage to an arbitrary position, rotation, and velocity, a control system calculates a necessary driving force from information on the current position, rotation, and velocity calculated on the basis of the measurement value of the laser interferometer and information on a target position, rotation, and velocity. The control system controls the stage to an arbitrary position, rotation, and velocity by driving an actuator attached to the stage in accordance with the calculated driving force.
In stage control, a measurement laser beam irradiates the surface of a bar mirror attached to the side surface of the stage, and reflected light is detected by the laser interferometer, measuring the stage position.
In this stage position measurement, the bar mirror is irradiated with a plurality of measurement laser beams having different optical axis positions along the same direction, and the stage position is measured at a plurality of positions. The difference between these measurement values is used to detect the rotation amount and inclination amount of the stage. For example, a plurality of measurement laser beams are arranged side by side in directions parallel and perpendicular to the driving plane of the stage. Calculation is done on the basis of the difference between these measurement values and the distance between the optical axes of the beams. The stage rotation amount is calculated from the difference between two measurement values in the horizontal direction, and the stage inclination amount is calculated from the difference between two measurement values in the vertical direction.
In a position sensor available at present, an error may be superposed on a measurement value owing to a kind of medium (for example, a kind of a gas) and fluctuations of magnetic field and electrical field, or the like, in a space between an object to be measured and the sensor main body. An error which makes the output nonlinear may occur also when the actual displacement of an object is a linear change. If the level of the nonlinear error changes depending on the individual difference in the sensor, the displacement in the rotational direction is calculated even upon translating the stage in, e.g., only the X direction when the rotation amount and inclination amount are calculated from the above-described difference among a plurality of axes.